Nuclear Magnetic Resonance (NMR) Spectroscopy is an important technique that allows determining protein structure in solution. An important problem in protein structure determination using NMR spectroscopy is the mapping of peaks to corresponding amino acids. Structure Based Assignment (SBA) is an approach to solve this problem using a template structure that is homologous to the target. Our previously developed approach NVR-BIP computed the optimal solution for small proteins, but was unable to solve the assignments of large proteins. NVR-TS extended the applicability of the NVR approach for such proteins, however the accuracies varied significantly from run to run.In this paper, we propose NVR-ACO, an Ant Colony Optimization (ACO) based approach to this problem. NVR-ACO is similar to other ACO algorithms in a way that it also consists of three phases: the construction phase, an optional local search phase and a pheromone update phase. But it has some important differences from other ACO algorithms in terms of solution construction and pheromone update functions and convergence rules. We studied the data set used in NVR-BIP and NVR-TS. Our new method finds optimal solutions for small proteins and achieves perfect assignment on EIN and higher accuracy on MBP compared to NVR-TS. It is also more robust.